7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Kinetic dispersion theory of linear dispersion relations in anisotropic plasmas:
An alternative approach

G. Abbas1, G. Murtaza1,2, H. Fatima1, M. Shahid1, Z. Iqbal1, M. Sarfraz1, F. Anjum1 and Maryam1
1
Department of physics, Government College University Lahore, Pakistan
2
Department of physics, Forman Christian College University Lahore, Pakistane-mail (gohar.abbas@gcu.edu.pk):
Extensive research has been done over the years tostudy the dispersion properties of various waves andinstabilities considering simple Cartesian geometry or
Cartesian geometry parameterized with cylindricalcoordinates in such plasmas [1-7]. On the other hand,
there are some certain astrophysical and laboratory
plasma environments where the Cartesian geometry
parameterized in spherical polar coordinates is used to
explore the dispersion properties of the waves withanisotropy in momentum space. For example, thedispersion relations of high-temperature deconfinedstrongly interacting matter have been analyzed in asituation when there is an anisotropy in the momentumspace distribution function that plays an important role inthe dynamical evolution of quark-gluon plasma [8,9]. A
linear dispersion relation for an unmagnetizedelectromagnetic wave in ultra-relativistic anisotropic
plasma with arbitrary temperature degeneracy have also
been derived [10]. Such a study is reported to be importantdue to the desirable accounting for plasma oscillations on
the dielectric constant including electron degeneracy andscreening in the context of white dwarfs and neutron stars[11]. In the present investigation, we consider the particle
distribution function of the form 𝑓₀(∣ 𝑝 ∣) = 𝑓₀(√(𝑝² +𝜉(𝑝. 𝑛)²)) and derive the dielectric tensor to revisit
longitudinal and transverse waves for the relativistic
anisotropic plasmas. Compared to the previously known
standard results derived using cylindrical coordinate
systems, the present study may prove to be an important
addition in the form of velocity integrals. The study may
also prove to be important for the evaluating the plasma
response functions for the regions where the relativistic
effects predominantly exist with temperature anisotropy.
The analysis may also be important in the regions wherethe plasma expands spherically. For example, a highpower laser that irradiates a spherical plasma where theanisotropy in the electron distribution function
predominantly exists [12]. This is mainly due to thehomogeneous heating of the plume by the energetic
species giving rise to the anisotropic expansion of theplasma [13].

1984)[2] S. Ichimaru, Basic Principles of Plasma Physics(Addison- Wesley Press, Tokyo, 1973)[3] M. Brambilla, Kinetic Theory of Plasma Waves
Homogeneoues plasmas (Oxford University Press, NewYork, 1998)[4] M. Miyamoto, Plasma Physics for Nuclear Fusion(MIT Press, New York, 1980)[5] A. F. Alexandrov, L. S. Bogdankevich, A.A.
Rukhadze, Principles of Plasma Electrodynamics(Springer-Verlag Berlin Heidelberg Press, New York,1984)[6] D. C. Montgomery, D. A. Tidman, Plasma Kinetic
Theory (McGraw-Hill Press, New York, 1964)[7] A. Bret, M.C. Firpo, C. Deutsch, Phys. Rev. E. 70,046401 (2004).
[8] P. Romatschke and M. Strickland, Phys. Rev. D 68,036004 (2003).
[9] P. Romatschke and M. Strickland, Phys. Rev. D 70,116006 (2004).
[10] M. Sarfraz, H. Farooq, G. Abbas, S. Noureen, Z.
Iqbal, and A. Rasheed, Phys. Plasmas 25, 032106 (2018).
[11] A. Beck and F. Pantellini, Plasma Phys. Control.
Fusion 51 015004 (2009).
[12] S. Eliezer, The Interaction of High-Power Lasers
with Plasmas, (Institute of Physics Publishing, Bristol,UK, 2002)[13] W. L. Kruer, The physics of laser plasmainteractions. (United States: Addison-Wesley Pub Co Inc.
1988).

References
Fig.1 of the manuscript (submitted for publication)[1] F. F. Chen, Introduction to Plasma Physics andControlled Fusion, vol. 1 (Plenum Press, New York,

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